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more entropy

I've just finished reading God: The Failed Hypothesis by Victor J Stenger, and was wondering if somebody could clear something up for me.

One thing he said was that the definition of maximum entropy of a sphere (universe) was a black hole of the size of the sphere. Am I right in thinking he puts forth this definition because in the black hole, everything is uniform, at equilibrium? Same density, same temperature, same pressure.

If that is the case then for a moment I thought that minimum entropy would be a vacuum, but that actually seems to fit the above description of maximum entropy as well.

The minimum entropy would occur when you had the maximum temperature, mass distribution, energy, etc. gradients. So suppose everything was concentrated in roughly one point on the sphere, the gradients would be maximal and as the system evolved it would eventually continually redistribute until it reached the point of maximum entropy you mentioned.

Nam et ipsa scientia potestas est.
Explaining the universe by invoking god is like solving an equation by multiplying both sides with infinity. It gives you a trivial solution and wipes away any real information about the original problem.

this is my first post in this forum, and I'd like to respond to your question.

Actually I'm a student of physics and recently had to deal with statistical physics and

thermodynamics a lot.

The entropy of a system, say the univers, tells you something about the amount of information an observer has of this system. If the exact state of the system, for example the exact position and impulse of every single particle it is made of, is known to the observer, the systems entropy equals 0. So a maximum of information about the system means a minimum entropy.

If the state of the system is not known exactly (usually the case, for you can't at one moment meassure all the particles positions etc.) you can still have statistical information, i.e. mean values of physical quantities of the system, for example its temperature (that is the _mean_ value of the kinetic energy of the particles). given a specific temperature, there are many configurations (=states of the system) of impulses and positions of the particles that would all give the same _mean_ kinetic energy. So knowing the systems temperature the observer doesn't know the exact state of the system, but that it has to be one of these many states. therefore the information about the system has decreased, its entropy has increased.

Finally, If the systems state is totally unknown, its entropy is at a maximum.

This said, I think the reason why Stenger says that a black hole is a system of maximum entropy is because you can't know the state of the hole, because no information can escape the hole to tell an observer of its state.

To say that a vacuum has minimum entropy, I think, is not correct, because by definition a vacuum is not a system at all. ^^

"And the only people I fear are those who never have doubts."
Billy Joel, 1993